Dipolar Coupling and Solids NMR BCMB/CHEM 8190 Liquids v. Solids One can collect similar spectra but some tricks are required 13C solution, sat’d glucose, 8 min 13C CP-MAS, 30 mg cellulose, 9 min The Classical Dipole-Dipole Interaction: z θ B0 μ1 θ r r μ2 x φ y E = (μ0/4π)(( μ1· μ2)/r3 – 3(μ1· r)( μ2·r)/r5) r = i rx + j ry + k rz = i r sinθcosφ + j r sinθsinφ + k r cosθ Quantum Mechanical Dipolar Coupling μ = (γh/2π)(i Ix + j Iy + k Iz) = (γh/2π)f(Iz, I+,-) HD = (μ0γ1γ2h2)/(16π3r3)(A + B + C + D + E + F) A,B,C .. Grouped by type of operator, 0,1,2 Quantum A = - Iz1Iz2(3cos2θ - 1), B = (1/4)(I+1I-2 + I-1I+2) (3cos2θ - 1) ……….. E = -(3/4)(I+1I+2)sin2θexp(-2iφ), F = …….. To First Order Only Iz1Iz2 Term is Important A doublet would result – much like scalar coupling but large: as much as -60,000 Hz for a 13C-1H pair. Splittings are angle dependent – ranging from -60,000 to +30,000. In a solid all possibilities superimpose: The result is a powder pattern Points at 90º on a sphere are most abundant D Other Anisotropies in NMR H = HCSA + HD + HQ... All share the following property: Solution: < 3 cos 2 θ '– 1 > = 0 Solids: (3 cos 2 θ ' – 1) ≠ 0 CSA powder pattern Techniques in Solids NMR • Cross Polarization (CP) • Magic Angle Spinning (MAS) • High power decoupling Cross Polarization Improves Sensitivity Magnetization transfer via dipolar coupling. Hartman-Hahn: γIBI = γSBS Magic Angle Spinning • All interactions can be written in terms of Y20(θ) = (3cos2(θ)–1)/2 • Y20(θ) can be transformed to another frame using Wigner Rotation elements: Y20(θ) = Σ2m=-2 D2m0(θ’’,φ’’) Y2m (θ’,φ’) • D2m0(θ’’,φ’’) = (4π/5) Y2m (θ’’,φ’’) • With rapid averaging over φ’’, all terms except Y20(θ’’) go to zero • Selecting θ’’ = 54.7°, all interactions, regardless of θ’ value, are zero • (3cos2(θ)–1) = (3cos2(θ’)–1) <3cos2(54.7°)–1> = 0 Dipolar couplings CSA Quadrupolar couplings = 0 φ’’ X Z θ’’ θ’ θ Y Bo θ 100 MHz Spectrometer with HFC Transmission-Line Probe • 100 MHz Spectrometer High power decoupling Solution 13C-1H J Solid 13C-1H J + D = ~125 kHz = ~125 Hz Cellulose (10 minute spectra) What is this peak? 13C Spinning Sidebands are Frequently Seen When rotation rate is not >> anisotropies Resonance position is modulated by rotation Sidebands at the spinning frequency are produced There are tricks that remove these: TOSS – Total Suppression of Spinning Sidebands 180º pulses during rotor cycle dephases sideband magnetization but preserves center band magnetization Peptide 1,2-13C2-Gly (9 minute spectra) Biomolecular Applications Spider Silk Nephila edulis Nature as Engineer • • • • Strongest fiber β-sheet Poly-Ala = crystalline Poly-Gly = amorphous Spider Silk and SS-NMR • • • Torsion angle pairs to resolve backbone structure Ala in two different environments Dynamics Ψ Φ Rhodopsin • Absorbs light in visible region • Binds retinal Rhodopsin in simulated bilayer Theoretical and Computational Biophysics Group, Schulten Laboratory Univ. Illinois Urbana-Champaign http://www.blackwellscience.com/matthews/rhodopsin.html Antibiotics & bacterial growth Schaefer Laboratory, Washington University, St. Louis, MO New Solids NMR Assignment Strategies Parallel Solution Methods Aliphatic region of the 13C,13C CP MAS PDSD of Zn-MMP-12 (16.4 T, 11.5 kHz MAS frequency, 15 ms mixing time). (Balayssac, Oschkinat, 2007) Annual Reviews 2D solid-state NMR spectra of uniformly 15N,13C-labeled Aβ1-40 amyloid fibrils. (a) 2D 13C-13C NMR spectrum, obtained in a 14.1-T magnetic field with 13.6-kHz magic-angle spinning, using a 2.94-ms finite-pulse radiofrequency-driven recoupling (fpRFDR) sequence for spin polarization transfer in the mixing period. (b) 2D 15N-13C spectrum, obtained with frequency-selective 15N-13C cross-polarization followed by fpRFDR in the mixing period. SOLIDS NMR REFERENCES Ashida, J., Ohgo, K., Komatsu, K., Kubota, A., and Asakura, T. (2003). Determination of the torsion angles of alanine and glycine residues of model compounds of spider silk using solid-state NMR methods. J. Biomol. NMR 25, 91-103. Kim, S.J., Cegelski, L., Studelska, D.R., O'Connor, R.D., Mehta, A.K., and Schaefer, J. (2002). Rotational-echo double resonance characterization of vancomycin binding sites in Staphylococcus aureus. Biochemistry 41, 6967-6977. Grobner, G., Burnett, I.J., Glaubitz, C., Choi, G., Mason, A.J., and Watts, A. (2000). Observations of light-induced structural changes of retinal within rhodopsin. Nature 405, 810-813. Solid-state NMR of matrix metalloproteinase 12: An approach complementary to solution NMR (2007) Balayssac S, Bertini I, Falber K, Oschkinat, H, et al. CHEMBIOCHEM 8 486-489. Solid-State NMR Studies of Amyloid Fibril Structure (2011) Tycko R. Ann. Rev. Phys. Chem. 62, 279-299. Recent contributions from solid-state NMR to membrane protein structure and function, Judge, PJ and Watts, A, (2011) Cur. Opin. Chem. Biol. 15, 690-695.